Logic Gates

• Logic Gates: They take binary inputs and give binary outputs in an electronic circuit.

• Truth Table: A table used to check the outputs from a logic gate or logic circuit.

  • All possible combinations of binary inputs are considered in a Truth Table.

• The six different types of Logic Gates are as follows:

• NOT Gate: Has only one input and output is 1 only if input is 0.

  

  • Truth Table:

• AND Gate: Two inputs. Output is 1 if both inputs are 1s.

  

  • Truth Table:

• Tip: Multiply the inputs.

• OR Gate: Two inputs. Output is 1 when any of the inputs is 1.

  

  • Truth Table:

• Tip: Add the inputs.

  

• NAND (NOT AND) Gate: Two Inputs. Output is 1 if both inputs are not 1.

  

  • Truth Table:

• Tip: Calculate for AND and write opposite output.

  

• NOR (NOT OR) Gate: Two inputs. Output is 1 if neither input is 1

  

  • Truth Table:

• Tip: Calculate for OR and write opposite.

  

• XOR Gate: Two inputs. Output is 1 if inputs are not same.

  

  • Truth Table:

Logic Circuits

• Multiple Logic gates make up a Logic Circuit.

• Complex operations are performed through them.

• Truth tables are made to check outputs, and all inputs are considered.

• To make a truth table, it is easier to divide the circuit into parts and name all the outputs at each stage.Example:

• In order to make a Logic Circuit from a Logic statement, mark all the gates in the statement, and always mind the brackets.

• To make a logic circuit from Boolean or Logic statements, make different parts of the circuit and then join them using gates which connect the brackets.

• Some logic gates can make a whole logic circuit and any other logic gate. They are known as Building Blocks. NAND gate, for example, can make an AND gate:

  

• Logic circuit can also be simplified. Just like the circuit above can be simplified to just one AND gate.

• Note: When one input branches into two before entering a gate, the two branched inputs will always be same. 1,1 or 0,0.